Regarding your first point, the idea is that if the US economy tanked or crashed Lyft would be utterly screwed but Uber might be able to ride (haha) it out with revenue from its non-US markets. In reality, if anything that bad happened to the US the rest of the developed is most likely screwed too, but that's the concept.
As for your second point, you might be right. It's not EVERY point of market share, but it must still be a significant number that is wrested from Uber with great difficulty.
Taking Lyft to be a single-purpose undiversified company, isn't the opposite true? I'm no economist nor MBA, but aside from cashflow wouldn't a smaller company be more resilient to conditions due to lower resource demands?
every point of marketshare they get is a zero-sum game against Uber
Is this...true? First, because there's more than two players in the industry, and second because there can be more demand than cars among all of them.